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Full text of "Mathematical And Physical Papers - Iii"

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To examine more particularly the mode of action, let P be any particle of dust, and consider a wave of light which emanates from any particular element of the flame or source of light whatever it be.   When this wave reaches P and proceeds along it, "a portion is reflected externally in all directions, and with this we have nothing more to do.    When the wave has just passed P, we may conceive it as having in a certain sense a hole in its front, corresponding in size to P, that is to say, there will be a certain portion of the surface forming the general front of the wave where the ether is quiescent.    As the wave proceeds, the disturbance diverges from the neighbourhood of this hole by regular diffraction, and when the disturbance reaches the quicksilvered surface the general wave suffers reflection, as well as the secondary waves, which, having diverged from the neighbourhood of P, do not constitute a wave with an unruffled front, in consequence of the absence of secondary waves diverging from the hole, which would be necessary to complete a wave with a front similar to that of the original wave.    If we consider any particular diffracted ray, the chances are that on its return it will get out by regular refraction, since the dust is supposed to cover a moderate portion only of the first surface of the mirror.    A portion of the original wave which entered the glass by regular refraction at a certain distance from P, after regular reflexion is incident on P from within.    The chances are that the portion thus incident on P does not correspond to a spot where the front of the wave is materially ruffled by diffraction at entrance, so that in considering the wave incident on P we may neglect   the   previous  diffraction.     The   wave,   then, just  after refraction, is incident on P, by which a portion is reflected back again in various directions, with which we have nothing to do, a portion, it may be, is  refracted or absorbed by P, and  the remainder passes on.    The  wave  so  passing  on   diverges  from the  neighbourhood of P by ordinary diffraction,  and  the  two diffracted streams, having been diffracted in a similar manner by the same particle, are in a condition to interfere.    The similarity of the two diffractions will be considered in more detail in the next section.
Now while the light is still in the glass conceive the particles of dust removed, and then replaced at random. The chances are that no particle will now occupy the position formerly occupied by